The Bright Star in the globular cluster 47 Tucanae (NGC 104) is a post-AGB star of spectral type B8 III. The ultraviolet spectra of late-B stars exhibit a myriad of absorption features, many due to species unobservable from the ground. The Bright Star thus represents a unique window into the chemistry of 47 Tuc. We have analyzed observations obtained with the Far Ultraviolet Spectroscopic Explorer (FUSE), the Cosmic Origins Spectrograph (COS) aboard the Hubble Space Telescope, and the MIKE Spectrograph on the Magellan Telescope. By fitting these data with synthetic spectra, we determine various stellar parameters (T_eff = 10,850 +/- 250 K, log g = 2.20 +/- 0.13) and the photospheric abundances of 26 elements, including Ne, P, Cl, Ga, Pd, In, Sn, Hg, and Pb, which have not previously been published for this cluster. Abundances of intermediate-mass elements (Mg through Ga) generally scale with Fe, while the heaviest elements (Pd through Pb) have roughly solar abundances. Its low C/O ratio indicates that the star did not undergo third dredge-up and suggests that its heavy elements were made by a previous generation of stars. If so, this pattern should be present throughout the cluster, not just in this star. Stellar-evolution models suggest that the Bright Star is powered by a He-burning shell, having left the AGB during or immediately after a thermal pulse. Its mass (0.54 +/- 0.16 M_sun) implies that single stars in 47 Tuc lose 0.1--0.2 M_sun on the AGB, only slightly less than they lose on the RGB.